The overall objective of this work is to develop mathematical models and applications that will lead to correct definitions of genes and antigens in immunogenetic systems. A specific objective is to provide means for drawing inferences about genes, antigens, antibodies and specificities from serological or cell-mediated cytotoxicity data. The means for drawing inferences include discrete (combinatorial) models for experimental design and their logical analysis. An adequately developed model will provide a basis for handling and understanding large sets of data, for employing computing machinery effectively, and for developing an appropriate immunogenetic symbolism. A major interest is the extent to which phenomena and (physical) genetic models are a product not only of experimental data but of the symbolism used to structure the data. In addition, an investigation of existing data using the models already developed will be carried out. The precise relationship of specific genes to disease depends on their correct definition. It is essential for effective protein and nucleotide sequencing of the genes in question that symbolic representations correspond exactly with their physical counterparts.